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Quantum errors are primarily detected and corrected using the measurement ofsyndrome information which itself is an unreliable step in practical errorcorrection implementations. Typically, such faulty or noisy syndromemeasurements are modeled as a binary measurement outcome flipped with someprobability. However, the measured syndrome is in fact a discretized value ofthe continuous voltage or current values obtained in the physicalimplementation of the syndrome extraction. In this paper, we use this "soft" oranalog information without the conventional discretization step to benefit theiterative decoders for decoding quantum low-density parity-check (QLDPC) codes.Syndrome-based iterative belief propagation decoders are modified to utilizethe syndrome-soft information to successfully correct both data and syndromeerrors simultaneously, without repeated measurements. We demonstrate theadvantages of extracting the soft information from the syndrome in our improveddecoders, not only in terms of comparison of thresholds and logical error ratesfor quasi-cyclic lifted-product QLDPC code families, but also for fasterconvergence of iterative decoders. In particular, the new BP decoder with noisysyndrome performs as good as the standard BP decoder under ideal syndrome.

Soft Syndrome Decoding of Quantum LDPC Codes for Joint Correction of Data and Syndrome Errors